苏州2021几何拓扑会议——报告安排表

苏州2021几何拓扑会议——腾讯会议信息

会议主题：苏州2021几何拓扑会议(11.6-7)

会议时间：2021/11/06-2021/11/07 08:00-17:30(GMT+08:00) 中国标准时间 - 北京, 每天

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会议 ID：924 8871 8206会议密码：202111

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苏州2021几何拓扑会议

报告摘要

报告人：陈海苗（Haimiao Chen北京工商大学Beijing Technology and Business University）

报告题目：-character varieties of two-generator groups

摘要：For any group  with two generators, we develop a method for determining its SL(3;C)-character variety, which parameterizes conjugacy classes of irreducible representations

.

As an application, we find the -character variety for each double twist link by explicitly writing down the defining equations.

报告人：陈史标（Ser Peow Tan新加坡国立大学National University of Singapore）

报告题目：Prime orthogeodesics, concave cores and families of identities on hyperbolic surfaces

摘要：In this talk, we will explain how to obtain a family of identities relating lengths of curves and orthogeodesics of hyperbolic surfaces. These identities hold over a large space of metrics including ones with hyperbolic cone points, and in particular, show how to extend the Basmajian identity to surfaces with cusps or cone points. To do this, we consider the concave core of the surface which is obtained by removing the natural collar neighborhoods of the boundary components and we show how to partition the set of orthogeodesics into sets depending on their dynamical behavior, which can be understood geometrically by relating them to geodesics on orbifold surfaces (model surfaces). In particular, for the four holed sphere, our family of identities interpolates between the Basmajian and the McShane identities with these two identities occurring at the extreme points of the family, and non-trivial identities are also obtained for the thrice-punctured sphere. This is joint work with Ara Basmajian and Hugo Parlier.

报告人：李琼玲（Qiongling Li陈省身数学研究所 Chern Institute of Mathematics）

报告题目：Projective structures with holonomy in (quasi-)Hitchin representations

摘要：Higher Teichmüller theory is a generalization of Teichmüller theory to higher rank Lie groups. Hitchin and quasi-Hitchin representations generalize the Fuchsian and quasi-Fuchsian representations to higher rank Lie groups respectively. In this talk, we study the topology of manifold admitting real or complex projective structures with holonomy in (quasi)-Hitchin representations of surface groups into the Lie group  or . This is joint work with Daniele Alessandrini and Colin Davalo.

报告人：李友林（Youlin Li上海交通大学 Shanghai Jiao Tong University）

报告题目：Nonexistence and existence of fillable contact structures on 3-manifolds

摘要：In the first part, we construct infinitely many closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space two-component links. In the second part, we show that Dehn surgeries along certain knots and links, including those considered in the first part, admit Stein fillable contact structures as long as the surgery coefficients are sufficiently large. This is joint work with Fan Ding and Zhongtao Wu.

报告人：林剑锋（Jianfeng Lin清华大学 Tsinghua University）

报告题目：Exotic phenomena on 4-manifolds that survive a stabilization

摘要：Starting in dimension 4, there is a significant difference between the category of smooth manifolds and the category of topological manifolds. Such phenomena are called the "exotic phenomena". In 1960s, Wall discovered an important principle: all exotic phenomena on 4-manifolds will disappear after sufficiently many stabilizations (i.e. connected sum with the product of two spheres). Since then, it has been a fundamental problem to search for exotic phenomena that survives one stabilization. In this talk, we will show that such phenomena actually exist by proving the following two results:

(1) There exists a pair of diffeomorphisms on a 4-manifold that are topologically isotopic but not smoothly isotopic even after one stabilization.

(2) There exists a pair of properly embedded surfaces in a 4-manifold with boundary which are topologically isotopic but not smoothly isotopic even after one stabilization (part of talk is based on a joint work with Anubhav Mukherjee).

报告人：刘毅（Yi Liu北京国际数学研究中心 BICMR）

报告题目：Finite quotients, arithmetic invariants, and hyperbolic volume

摘要：In this talk, I will discuss the question as to determine geometric properties of orientable closed hyperbolic 3-manifolds by the finite quotients of their fundamental groups. I will explain an approach to match up the (Zariski-dense algebraic)  representations of a pair of those groups, up to conjugacy, if there is an isomorphism between their profinite completions. Assuming the -adic Borel regulator injectivity conjecture, one may deduce that the hyperbolic volume, the invariant quaternion algebra, and the arithmeticity are profinite properties.

报告人：马继明（Jiming Ma复旦大学 Fudan University）

报告题目：Schwartz's complex hyperbolic surface

摘要：Richard Schwartz considered an arithmetic, geometrically finite, discrete subgroup of the isometry group of the two dimensional complex hyperbolic space in 2003. Schwartz determined the 3-manifold at infinity of this group via a sophisticated method. More precisely, the 3-manifold at infinity is a closed hyperbolic 3-orbifold with underlying space the 3-sphere whose singularity locus is a two-components link. We determine the 4-dimensional topology of the complex hyperbolic surface of this group via the handle structure.

报告人：邱杨（Yan Qiu加州大学圣巴巴拉分校UCSB）

报告题目：From 3-manifolds to modular tensor categories

摘要：The progress of TQFT has revealed connections between the algebraic world of tensor categories and the topological world of 3-manifolds, such as Reshetikhin-Turaev and Turaev-Viro theories. Motivated by -theory in physics, Cho-Gang-Kim recently proposed another relation by outlining a program to construct modular tensor categories from certain classes of closed oriented 3-manifolds. In this talk, I will talk about our mathematical exploration of this program. This talk is based on the joint works [Cui-Qiu-Wang, arXiv: 2101.01674] and [Cui-Gustafson-Qiu-Zhang, arXiv: 2106.01959].

报告人：苏伟旭（Weixu Su复旦大学 Fudan University）

报告题目：Random hyperbolic surfaces obtained by gluing ideal triangles

摘要：Let  be an oriented surface of genus  with  punctures, where  and . Any ideal triangulation of  induces a global parametrization of the Teichmüller space called the shearing coordinates. We study the asymptotics of the number of the mapping class group orbits with respect to the standard Euclidean norm of the shearing coordinates. The work is jointed with Sicheng Lu.

报告人：孙哲（Zhe Sun法国高等科学研究所IHES）

报告题目：Skein algebras, webs and tropical points

摘要：The study of skein algebras is related to the study 3-manifold. On the other hand, finding the linear basis of a certain skein algebra is very important in representation theory. For , Kuperberg introduced oriented 3-valent graphs on the surface, called -webs, to study the -invariant tensor products  of irreducible representations of . Actually, these webs generate  skein algebra. Then Kuntson-Tao found a family of linear inequalities to characterize when  contains an invariant vector for . Let A be a variation of the  character variety which generalizes the Penner's decorated Teichmuller space. Observed by Goncharov-Shen, these inequalities can be identified by the positivity of a potential function, which characterizes a discrete subset  of the real tropicalization of . On the surface, we identify the space of -webs up to homotopy with  mapping class group equivariantly. As a consequence, as predicted by Fock-Goncharov duality conjecture, these tropical points parameterize a linear basis of the regular function ring of the  character variety explicitly. This is a joint work with Daniel Douglas for  and ongoing joint work with Linhui Shen and Daping Weng for general .

报告人：田垠（Yin Tian北京师范大学 Beijing Normal University）

报告题目：Higher dimensional Heegaard Floer homology and Hecke algebras

摘要：Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It’s partly used to study contact topology in higher dimensions. In a special case, it’s related to symplectic Khovanov homology. In this talk, we discuss HDHF of cotangent fibers of the cotangent bundle of an oriented surface and show that it is isomorphic to various Hecke algebras. This is a joint work with Ko Honda and Tianyu Yuan.

报告人：王炜飚（Weibiao Wang北京大学 Peking University）

报告题目：Extending periodic automorphisms of closed surfaces to the 3-sphere

摘要：A periodic map on a surface is said to be extendable over the 3-sphere if there exists an embedding such that the surface map extends to a periodic automorphism of the 3-sphere. Inspired by some related work, Chao Wang and I give a complete classification of all extendable periodic maps for closed surfaces (in smooth category, with orientation-reversing cases included). In fact, we have constructed all such maps up to conjugacy.

报告人：吴云辉（Yunhui Wu清华大学 Tsinghua University）

报告题目：Recent developments on random hyperbolic surfaces of large genus

摘要：The overall behavior of quantities such as systole, eigenvalues of Laplacian, diameter, etc., for all closed hyperbolic surfaces is a classical object of study. We discuss several asymptotic results on these quantities viewed as random variables on the moduli space of Riemann surfaces for large genus, which was initiated by Mirzakhani in 2013. This talk is based on several joint works with Hugo Parlier, Xin Nie and Yuhao Xue.

报告人：杨田（Tian Yang德州农工大学 Texas A&M University）

报告题目：Hyperbolic geometry and quantuminvariants

摘要：There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston, and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.

报告人：杨文元（Wenyuan Yang北京国际数学研究中心 BICMR）

报告题目：Proper actions of 3-manifold groups on finite product of quasi-trees

摘要：Let  be a compact, connected, orientable 3-manifold. In this talk, I will study when the fundamental group  of  acts properly on a finite product of quasi-trees. Our main result is that this is so exactly when  does not contain Sol and Nil geometries. In addition, if there is no

 geometry either, then the orbital map is a quasi-isometric embedding of . This is called property (QT) by Bestvina-Bromberg-Fujiwara, who established it for residually finite hyperbolic groups and mapping class groups. The main step of our proof is to show property (QT) for the classes of Croke-Kleiner admissible groups and of relatively hyperbolic groups under natural assumptions. Accordingly, this yields that graph 3-manifold and mixed 3-manifold groups have property (QT). This represents joint work with N.T. Nguyen and S.Z. Han.

报告人：余斌（Bin Yu同济大学 Tongji University）

报告题目：Anosov flows on Dehn surgeries on the figure-eight knot

摘要：We will talk about classifying Anosov flows on the 3-manifolds obtained by Dehn surgeries on the figure-eight knot.